3 D-HQAM Constellation Design and Performance Evaluation Under AWGN

Abstract

This letter proposes a simple and effective method for constructing higher-order three-dimensional (3D) signal constellations. The proposed approach introduces a novel 3D hexagonal quadrature amplitude modulation (3D-HQAM) scheme, where constellation points are systematically arranged in a 3D signal space to form structured lattice configurations. To address the increased decision complexity resulting from a larger number of constellation points, a dimension reduction (DR) technique is introduced, allowing the derivation of an analytical approximation of symbol error probability (SEP) under additive white Gaussian noise (AWGN) conditions. Theoretical SEPs closely match simulation results, thereby validating accuracy of the proposed method. The minimum Euclidean distance (MED) of the 3D constellations shows a minimum increase of 12.14% over 2D constellation for 8-HQAM, reaching up to 160.81% for 1024-HQAM constellations. This significant improvement in MED leads to enhanced error performance. Additionally, the average SEP performance of the proposed system is analyzed over Rayleigh faded channel. Therefore, the proposed 3D constellations are promising candidates for high-quality and reliable next-generation digital communication systems. © 2012 IEEE.